Abstract
While adaptive cancer therapy is beginning to prove a promising approach of building evolutionary dynamics into therapeutic scheduling, the stochastic nature of cancer evolution has rarely been incorporated. Various sources of random perturbations can impact the evolution of heterogeneous tumors. In this paper, we propose a method that can effectively select optimal adaptive treatment policies under randomly evolving tumor dynamics based on Stochastic Optimal Control theory. We first construct a stochastic model of cancer dynamics under drug therapy based on Evolutionary Game theory. That model is then used to improve the cumulative ''cost'', a combination of the total amount of drugs used and the time to recovery. As this cost becomes random in a stochastic setting, we maximize the probability of recovery under a pre-specified cost threshold (or a ''budget''). We can achieve our goal for a range of threshold values simultaneously using the tools of dynamic programming. We then compare our threshold-aware policies with the policies previously shown to be optimal in the deterministic setting. We show that this threshold-awareness yields a significant improvement in the probability of under-the-budget recovery, which is correlated with a lower general drug usage. The particular model underlying our discussion has originated in [Kaznatcheev et al. 2017], but the presented approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.
Competing Interest Statement
The authors have declared no competing interest.
